A382681 Conjecturally, the numbers k (not multiples of 5) such that for all x >= 0, k*2^x has a '0' in its decimal expansion.

7501221, 7508793, 10006109, 10625334, 12970254, 15002442, 15017586, 15685077, 17975049, 20012218, 20752359, 21250668, 22500771, 23501007, 24625029, 24875024, 25033207, 25034183, 25034771, 25940508, 29003907, 29057504, 29450021, 29590047, 29625044, 29850293, 30004884, 30035172, 30175941

Offset: 1

Author

Brian Kehrig, Jun 02 2025

Keywords

• nonn
• base

Comments

If k is a multiple of 5, then k*2^x always ends with '0' for x >= 1. We exclude these trivial cases.

If k is in this sequence, then so is k*2^x for all x >= 1.

All terms up to 30175941 have been tested up to x=10^6.

Examples

			7501221*2^0 = 7501221 contains a '0'
7501221*2^1 = 15002442 contains a '0'
7501221*2^2 = 30004884 contains a '0'
7501221*2^3 = 60009768 contains a '0'
7501221*2^4 = 120019536 contains a '0'
7501221*2^5 = 240039072 contains a '0'
...
Conjecturally, all further numbers of the form 7501221*2^k also contain '0'. Thus, 7501221 is in the sequence.
		

Crossrefs

Cf. A007377, A027870, A130694.